Development of Regional Flood Frequency Relationships Using L-moments for Middle Ganga Plains Subzone 1(f) of India

In this study, screening of the data has been carried out basedon the discordancy measure (D _i) in terms of the L-moments. Homogeneity of the region has been tested using the L-moments based heterogeneity measure, H. For computing the heterogeneity measure H, 500 simulations were carried out using the four parameter Kappa distribution. Based on this test, it has been observed that the data of 8 out of 11 bridge sites constitute ahomogeneous region. Hence, the data of these 8 sites have been used in this study. Catchment areas of these 8 sites vary from 32.89 to 447.76 km² and their mean annual peak floods varyfrom 24.29 to 555.21 m³ s^-1. Comparative regional floodfrequency analysis studies have been carried out using the various L-moments based frequency distributions viz. Extreme value (EV1), General extreme value (GEV), Logistic (LOS), Generalized logistic (GLO), Normal (NOR), Generalized normal (GNO), Uniform (UNF), Pearson Type-III (PE3), Exponential (EXP),Generalized Pareto (GPA), Kappa (KAP), and five parameter Wakeby(WAK). Based on the L-moment ratio diagram and Z _i ^dist –statistic criteria, GEV distribution has been identified as the robust distribution for the study area. For estimation of floods of various return periods for gauged catchments of the study area, regional flood frequency relationship has been developed using the L-moments based GEV distribution. Also, for estimation of floods of desiredreturn periods for ungauged catchments, regional flood frequencyrelationship has been developed by coupling the regional flood frequency relationship with the regional relationship between mean annual maximum peak flood and catchment area.     

Regional Flood Frequency Analysis of North-Bank of the River Brahmaputra by Using LH-Moments

In this study LH-moment proposed by Wang (Water Resour Res 33(12):2841–2848, 1997) has been used for regional flood frequency analysis of the North-Bank region of the river Brahmaputra, India. Three probability distributions i.e. generalized extreme value (GEV), generalized logistic (GLO) and generalized Pareto (GPA) has been used for each level of LH-moments i.e. L, L₁, L₂, L₃ and L₄. The regional frequency analysis procedure proposed by Hosking and Wallis (Water Resour Res 29(2):271–281, 1993) for L-moments i.e. discordancy measure for screening the data, heterogeneity measure for formation of homogeneous region and goodness-of-fit test have been used for each level of LH-moments. Based on the LH-moment ratio diagram and ∣Z∣-statistic criteria, GEV distribution for level one LH-moment is identified as the robust distribution for the study area. For estimation of floods of various return periods for both gauged and ungauged catchments of the study area, regional flood frequency relationships have been developed by using the level one LH-moment based on GEV distribution. A comparative study has been performed between L-moments and LH-moments for the study area. It is observed from comparative study that the regional flood frequency analysis based on the GEV distribution by using level one LH-moment (L₁) is superior to the use of L-moments.     

Local and regional flood frequency analysis based on hierarchical Bayesian model in Dongting Lake Basin,China

This study developed a hierarchical Bayesian(HB) model for local and regional flood frequency analysis in the Dongting Lake Basin,in China.The annual maximum daily flows from 15 streamflow-gauged sites in the study area were analyzed with the HB model.The generalized extreme value(GEV) distribution was selected as the extreme flood distribution,and the GEV distribution location and scale parameters were spatially modeled through a regression approach with the drainage area as a covariate.The Markov chain Monte Carlo(MCMC) method with Gibbs sampling was employed to calculate the posterior distribution in the HB model.The results showed that the proposed HB model provided satisfactory Bayesian credible intervals for flood quantiles,while the traditional delta method could not provide reliable uncertainty estimations for large flood quantiles,due to the fact that the lower confidence bounds tended to decrease as the return periods increased.Furthermore,the HB model for regional analysis allowed for a reduction in the value of some restrictive assumptions in the traditional index flood method,such as the homogeneity region assumption and the scale invariance assumption.The HB model can also provide an uncertainty band of flood quantile prediction at a poorly gauged or ungauged site,but the index flood method with L-moments does not demonstrate this uncertainty directly.Therefore,the HB model is an effective method of implementing the flexible local and regional frequency analysis scheme,and of quantifying the associated predictive uncertainty.     

Regional Flood Frequency Analysis Using L-Moments for the West Mediterranean Region of Turkey

The aim of this study is to investigate and determine hydrologically homogeneous regions and to derive regional flood frequency estimates for 47 gauged sites in the West Mediterranean River Basins in Turkey, using an index flood method with L-moments parameter estimation. Screening of the data of the gauged site is carried out based on a discordancy measure in terms of the L-moments. Initial candidate regions are established by the cluster analysis of first five L-moment statistics, using k-means method. Homogeneity of the basins is tested using simulation with a four-parameter Kappa distribution and an L-moments based heterogeneity measure. Three subregions are defined, namely the Antalya subregion, the Lower West Mediterranean subregion, and the Upper West Mediterranean subregion. Comparative regional flood frequency estimates are made for each subregion using various distributions, namely the generalized logistic, general extreme value, generalized normal, Pearson type III, generalized Pareto, kappa, and Wakeby distributions. Based on an L-moments goodness-of-fit statistic, the Pearson type III distribution is identified as the best-fit distribution for the Antalya and Lower-West Mediterranean subregions, and the Generalized Logistic for the Upper-West Mediterranean subregion. Monte Carlo simulation is used to evaluate the accuracy of the quantile estimates on the basis of the relative root-mean-square error and relative bias.     

Regional Flood Frequency Analysis of Mahi-Sabarmati Basin (Subzone 3-a) using Index Flood Procedure with L-Moments

With the objective of investigating the hydrological homogeneity of India's hydrometeorological subzone 3-a and identification of a suitable frequency distribution for it, a regional flood frequency analysis has been carried out using the index flood procedure and the L-moments. Based on analysis of flood data at 12 gauged sites, the Mahi-Sabarmati basin is shown to be hydrologically homogeneous and follows the generalized normal distribution. Regional curve developed based on the analysis has been recommended for carrying out flood frequency analysis at both gauged and ungauged sites in this region.     

Regional Frequency Analysis of Extreme Rainfalls in the West Coast of Peninsular Malaysia using Partial L-Moments

This study was to reinstate the development of regional frequency analysis using L-moments approach. The Partial L-moments (PL-moments) method was employed and a new relationship for homogeneity analysis is developed. For this study, the PL-moments for generalized logistic (GLO), generalized pareto (GPA) and generalized value (GEV) distributions were derived based on the formula defined by Wang (Water Resour Res 32:1767?C1771, 1996). The three distributions are used to develop the regional frequency analysis procedures. As a case of study, the Selangor catchment that consists of 30 sites which located on the west coast of Peninsular Malaysia has chosen as sample. Based on L-moment and PL-moment ratio diagrams as well as Z-test statistics, the GEV and GLO were identified as the best distributions to represent the statistical properties of extreme rainfalls in Selangor. Monte Carlo simulation shows that the method of PL-moments would outperform L-moments method for estimation of large returns period event.     

Regional Flood Frequency Analysis of the Seven Sites of Punjab, Pakistan, Using L-Moments

L-moments based regional flood frequency analysis has been carried out on the seven sites of Punjab, Pakistan. Discordancy measure in terms of L-moments has been used to screen the data on each of the seven sites. Homogeneity of the region has been tested using the L-moments based heterogeneity measure (H). H has been calculated using four parameter Kappa distribution with 500 simulations. In order to find the most suitable distribution for quantile estimates, a number of L-moments based frequency distributions, such as, generalized logistic (GLO), generalized extreme-value (GEV), generalized normal (GNO), Pearson type III (PE3), generalized Pareto (GPA) and five parameter Wakeby (WAK) distribution, have been used. Based on the L-moment ratio diagram and Z ^DIST statistic, three distributions; GNO, GPA and GEV have been identified as the suitable candidates for regional distribution. Accuracy measures for the estimated regional growth curves and quantiles have been calculated for the three candidate distributions, using Monte Carlo simulations. Simulations study showed that GNO distribution is the robust distribution with GPA as suitable alternative but GEV is not an appropriate distribution for the study area.     

历史洪水变化时矩法与线性矩法统计性能对比分析

1990年由Hosking等学者提出的线性矩法（method of L-moments）,是水文频率计算中参数估计的新方法,极值分布是水文频率计算中常用的分布,在频率计算中充分考虑历史洪水是我国设计洪水计算的重要经验。为此,简要介绍了线性矩的基本概念,分析了极值分布统计参数与线性矩的关系,通过统计试验对比分析了在历史洪水变化时矩法、线性矩法的统计性能。结果表明,线性矩法的参数比矩法的更稳定。     

L-Moment-Based Regional Frequency Analysis of Annual Extreme Precipitation and its Uncertainty Analysis

Estimation of precipitation amounts associated with different return periods is an important task for the planning and design of many types of infrastructures. In this study, regional frequency analysis based on L-moments is proposed to estimate the annual maximum daily precipitation quantiles in the Taihu basin, China. The Generalized Extreme Value (GEV) distribution is used to describe the frequency distributions of extreme rainfall events. At-site frequency analysis results based on L-moments are compared with those obtained from regional analysis. The 95% confidence intervals of estimated precipitation quantiles are calculated using Monte Carlo simulations (MCS). Uncertainty assessment results indicate that regional analysis is more robust and more accurate than at-site analysis. Furthermore, when conducting regional frequency analysis, the estimation of precipitation quantile confidence intervals can be simplified by assuming normality for the MCS results. The variation of the precipitation quantiles’ sample statistics for different return periods is expressed as a function of the return period. The proposed methods are useful for the Taihu Basin and are recommended for other regions.     

基于地区线性矩法对四川省水文频率分析的研究

为了促进地区线性矩法在水文频率分析领域的研究与应用并改进我国传统水文频率分析的研究成果,为四川省的防洪工作提供一定的参考,根据地区线性矩法的基本思想和原理,对四川省共计150个国家自动气象站点的年最大日降雨序列进行分析,对四川省进行水文气象一致性区域划分,并确定各区域的最优频率分布线型。根据各个一致性区域的最优频率分布线型,估算出各个站点不同重现期下的设计值。此外,还把地区线性矩法与传统水文频率分析法估算的结果进行比较分析。结果表明:四川省可以划分为9个水文气象一致性区域;水文气象一致性区域1区、2区、3区、5区、6区、7区、8区、9区的最优频率分布线型均为广义逻辑斯蒂分布(GLO),4区的最优频率分布线型为广义极值分布(GEV);水文气象一致性区域3区、4区、6区为主要暴雨区。随着重现期增大,利用传统方法得到的设计值总体偏低。     

Regional Flood Frequency Analysis in Tunisia: Identification of Regional Distributions

Best-fit distributions of floods in Tunisia are determined based on L-moment diagram and statistical tests. GEV and GLO distributions provided the best fit to seven and three regions of Tunisia respectively. In each homogeneous region, hierarchical approaches and regression models were developed for gauged and ungauged watersheds. The first two parameters of the distributions (GEV and GLO) were estimated from measured data while the third parameter was represented by the regional average value weighted by the record length of all stations in the region. The obtained parameters were correlated to the catchment size. Quantiles obtained by the proposed models were compared with those obtained using local conventional models. Statistical tests showed that the proposed models provided a much better agreement with observed floods than any of the conventional methods generally used in Tunisia.     

Regional Dry Spells Frequency Analysis by L-Moment and Multivariate Analysis

The spatial variation of the statistical characteristics of the extreme dry events, such as the annual maximum dry spell length (AMDSL), is a key practice for regional drought analysis and mitigation management. For arid and semi arid regions, where the data set is short and insufficient, the regionalization methods are applied to transfer at-site data to a region. The spatial variation and regional frequency distribution of annual maximum dry spell length for Isfahan Province, located in the semi arid region of Iran, was investigated using a daily database compiled from 31 rain gauges and both L-moment and multivariate analysis. The use of L-moment method showed a homogeneous region over entire province with generalized logistic distribution (GLOG) as the regional frequency distribution. However, the cluster analysis performed two regions in west and east of the province where L-moment method demonstrated the homogeneity of the regions and GLOG and Pearson Type III (PIII) distributions as regional frequency distributions for each region, respectively. The principal component analysis was applied on at-site statistics of AMDSL and found the L-coefficient of skewness (LCs) and maximum AMDSL the main variables describing the spatial variation of AMDSL over the Isfahan Province. The comparison of two homogeneous regions also proved the difference between two regions. Therefore, this study indicates the advantage of the use of multivariate methods with L-moment method for hydrologic regionalization and spatial variation of drought statistical characteristics.     

Estimating Temporal Changes in Extreme Rainfall in Sicily Region (Italy)

An intensification of extreme rainfall events have characterized several areas of peninsular and insular Italy since the early 2000s, suggesting an upward ongoing trend likely driven by climate change. In the present study temporal changes in 1-, 3-, 6-, 12- and 24-h annual maxima rainfall series from more than 200 sites in Sicily region (Italy) are examined. A regional study is performed in order to reduce the uncertainty in change detection related to the limited length of the available records of extreme rainfall series. More specifically, annual maxima series are treated according to a regional flood index - type approach to frequency analysis, by assuming stationarity on a decadal time scale. First a cluster analysis using at-site characteristics is used to determine homogeneous rainfall regions. Then, potential changes in regional L-moment ratios are analyzed using a 10-year moving window. Furthermore, the shapes of regional growth curves, derived by splitting the records into separate decades, are compared. In addition, a jackknife procedure is used to assess uncertainty in the fitted growth curves and to identify significant trends in quantile estimates. Results reveal that L-moment ratios show a general decreasing trend and that growth curves for the last decade (2000–2009) usually do not stand above the others, with the only exception of the ones related to the outer western part of Sicily. On the other hand, rainfall quantile estimates for the same period are the highest values almost all over the region. An explanation can be found in the increase of subregional average medians, largely caused by recent severe local storms.     

基于广义极值分布和Metropolis-Hastings抽样算法的贝叶斯MCMC洪水频率分析方法

广义极值（GEV）分布是国内外洪水频率分析建模中广泛应用的一种概率分布。本文将水文频率分布线型的未知参数看作随机变量，通过基于Metropolis-Hastings抽样算法的贝叶斯MCMC方法估计GEV分布参数和设计时段洪量的后验分布，并据此进行极值洪水的频率分析。汉江流域丹江口水库年最大1日（3日、5日、7日）洪量频率分析的结果表明了本方法的有效性和实用性。主要结论包括：基于Metropolis-Hastings抽样的MCMC模拟在GEV分布参数的贝叶斯估计计算中行之有效；由于利用了与似然函数渐近性质无关的先验信息，贝叶斯估计方法得到的高分位数设计洪量的后验分布比经典统计方法得到的设计洪量能包含更多的信息，从而能表达由于参数不确定性而引起的预测不确定性。该方法能显著地通过分位数图、PPCC法、均方根误差法、K-S法等多种拟合优度检验方法，拟合效果不亚于其他常用的经典统计方法。     

Comparison of Artificial Neural Network Methods with L-moments for Estimating Flood Flow at Ungauged Sites: the Case of East Mediterranean River Basin, Turkey

A regional flood frequency analysis based on the index flood method is applied using probability distributions commonly utilized for this purpose. The distribution parameters are calculated by the method of L-moments with the data of the annual flood peaks series recorded at gauging sections of 13 unregulated natural streams in the East Mediterranean River Basin in Turkey. The artificial neural networks (ANNs) models of (1) the multi-layer perceptrons (MLP) neural networks, (2) radial basis function based neural networks (RBNN), and (3) generalized regression neural networks (GRNN) are developed as alternatives to the L-moments method. Multiple-linear and multiple-nonlinear regression models (MLR and MNLR) are also used in the study. The L-moments analysis on these 13 annual flood peaks series indicates that the East Mediterranean River Basin is hydrologically homogeneous as a whole. Among the tried distributions which are the Generalized Logistic, Generalized Extreme Vaules, Generalized Normal, Pearson Type III, Wakeby, and Generalized Pareto, the Generalized Logistic and Generalized Extreme Values distributions pass the Z statistic goodness-of-fit test of the L-moments method for the East Mediterranean River Basin, the former performing yet better than the latter. Hence, as the outcome of the L-moments method applied by the Generalized Logistic distribution, two equations are developed to estimate flood peaks of any return periods for any un-gauged site in the study region. The ANNs, MLR and MNLR models are trained and tested using the data of these 13 gauged sites. The results show that the predicting performance of the MLP model is superior to the others. The application of the MLP model is performed by a special Matlab code, which yields logarithm of the flood peak, Ln(Q_T), versus a desired return period, T.     

Regional sub-hourly extreme rainfall estimates in Sicily under a scale invariance framework

Design of urban drainage systems or flood risk assessment in small catchments often requires knowledge of very short-duration rainfall events (less than 1 h). Unfortunately, data for these events are often unavailable or too scarce for a reliable statistical inference. However, regularities in the temporal pattern exhibited by storm records, known as scaling properties of rainfall, could help in characterizing extreme storms at partially gauged sites better than the application of traditional statistical techniques. In this work, a scaling approach for estimating the distribution of sub-hourly extreme rainfall in Sicily (Italy) is presented based on data from high-resolution rain gauges with a short functioning period and from low-resolution rain gauges with longer samples. First, simple scaling assumption was tested for annual maxima rainfall (AMR) data from 10 min to 24 h duration, revealing that the simple scaling regime holds from 20 to 60 min for most of the stations. Then, scaling homogeneous regions were classified based on the values of the scaling exponent. In each region, this parameter was regionalized through power-law relationships with the median of 1 h AMR data. After that, regional Depth Duration Frequency (DDF) curves were developed by combining the scale-invariant framework with the generalized extreme value (GEV) probability distribution and used to estimate T-year sub-hourly extreme rainfalls at sites where only rainfall data for longer durations (≥ 1 h) were available. The regional GEV simple scaling model was validated against sub-hourly historical observations at ten rain gauges, generally yielding, in relation to the scaling exponent value, to similar or better sub-hourly estimates than empirical approach.

     

Application of the Regional Flood Frequency Analysis to the Upper and Lower Basins of the Indus River,Pakistan

The paper presents results of an application of the L-moments based regional flood frequency analysis to annual maximum peak (AMP) flows observed at seven stations (Tarbela, Kalabagh, Chashma, Taunsa, Guddu, Sukkur and Kotri) located on the main stream of the Indus River, Pakistan. The results of Run-test and lag-1 correlation coefficient showed that the data series at given sites is random and has no serious serial correlations respectively. Furthermore, the results of Grubbs and Beck test illustrated that there are no irregularities (abrupt variations) except low outlier(s) in the data series at various sites. To avoid their undue influence, these low outliers have been discarded and the sample information has been re-summarized using the idea of left censored type A ^′ partial probability weighted moments. L-moments based regional heterogeneity measure (H) showed that the region, defined by seven stations, is heterogeneous; therefore, it has been sub-divided into two homogeneous regions (Region 1 and Region 2 consist of four (Tarbela, Kalabagh, Chashma and Taunsa) and three sites (Guddu, Sukkur and Kotri, respectively) using Ward’s clustering method based on the site characteristics only. The results of various goodness-of-fit measures (L-moment ratio diagram, average weighted distance and Z ^DIST measures) showed that Region 1 has four candidates: generalized normal (GNO), generalized logistic (GLO), generalized extreme-value (GEV) and Pearson type III (PE3), while Region 2 has only one candidate; GLO, as regional distribution. Based on the results of different accuracy measures (regional average absolute relative bias, relative bias and relative root mean square error) of the estimated regional growth curves and quantiles, obtained from simulation experiments, PE3 is the robust distribution for Region 1, while for Region 2, GLO distribution can be used for the estimation of flood quantiles. Moreover, the results of the simulations study have been extended to obtain standard errors of the estimated quantiles at each site of the sub-divided homogeneous regions.     

分布式单位线在河北雨洪模型中的应用

因河北雨洪模型的汇流计算方法难以用于无资料流域,其汇流参数难以获得且不宜移用,为此,将基于数字高程模型的分布式单位线用于河北雨洪模型,并对峪门口流域4场较大洪水过程进行了模拟。结果表明:4场洪水洪峰流量相对误差均<5%,峰现时间误差均<2 h,确定性系数均>0.85,模拟效果令人满意。河北雨洪模型与基于流域地形地貌特征的分布式单位线相结合,可解决无资料流域,特别是山丘地区中小流域的洪灾预警预报等问题。     

Frequency analysis of upper cauvery flood data by L-moments

The objectives of the present study are to investigate the hydrological homogeneity of Upper Cauvery annual maximum flow data and to select a suitable distribution for the frequency analysis. The L-moments method is used in this analysis. The Upper Cauvery river basin is shown to be hydrologically heterogeneous. The 3 parameter log normal and the generalized extreme value distributions are recommended for the frequency analysis of data in this region.